Learn Croatian: Imamo problem, nema više strpljenja za ovo. - We have a problem, there is no more patience for this.

This is the main rule of negative existence! When you use nema to mean 'there is no', the thing that is missing must be in the genitive case. The dictionary form is the neuter noun strpljenje (patience). To make it genitive, the final -e changes to -a, giving us strpljenja.

Does nema mean 'he doesn't have' or 'there is no' here?

In this sentence, it means 'there is no'. While nema is the 'he/she/it' form of the verb 'to not have', Croatian also uses it as a fixed phrase to say 'there isn't' or 'there is no'. You can tell from the context that we aren't talking about a specific person lacking patience.

Can I always pair nema with više to say 'there is no more'?

Yes! nema više is an extremely common phrase meaning 'there is no more' or 'there is none left'. Just remember that whatever is missing still needs to go into the genitive case right after it, like strpljenja in this sentence.

Why doesn't the word problem change its ending after imamo?

The verb imamo (we have) requires the accusative case because problem is the direct object. However, problem is a masculine inanimate noun (it is not a living thing). For masculine inanimate nouns, the accusative form is exactly the same as the dictionary form, so it doesn't change.